1.快速排序

思想：确定元素数据

void quick_sort(int q[],int l,int r){
	if(l >= r) return;

	int i = l - 1, j = r + 1, x = q[r + l >> 1];
	while(i < j){
		do i++; while(q[i] < x);
		do j--; while(q[j] > x);
		if(i < j) swap(q[i],q[j]);
	}

	quick_sort(q, l, j);
	quick_sort(q, j + 1, r);
}


2.归并排序

思想：确定索引

void merge_sort(int q[],int l,int r){
	//如果左侧索引大于等于右侧索引，直接返回原数组
	if(l >= r) return;
	//确定索引，一般取l,r,(l+r)/2
	int mid = l + r >> 1;
	//递归
	merge_sort(q, l, mid);
	merge_sort(q, mid + 1, r);

	int k = 0, i = l, j = mid +1;
	while(i <= mid && j <= r){
		if(q[i] < q[j]) tmp[k++] = q[i++];
		else tmp[k++] = q[j++];
	}

	while(i <= mid ) tmp[k++] = q[i++];
	while(j <= r) tmp[k++] = q[j++];

	for(int i = l, j = 0; i <= r ; i ++, j++) q[i] = tmp[j];
}

3.整数二分

bool check(int x) {/* ... */} // 检查x是否满足某种性质

// 区间[l, r]被划分成[l, mid]和[mid + 1, r]时使用：
int bsearch_1(int l, int r)
{
    while (l < r)
    {
        int mid = l + r >> 1;
        if (check(mid)) r = mid;    // check()判断mid是否满足性质
        else l = mid + 1;
    }
    return l;
}
// 区间[l, r]被划分成[l, mid - 1]和[mid, r]时使用：
int bsearch_2(int l, int r)
{
    while (l < r)
    {
        int mid = l + r + 1 >> 1;
        if (check(mid)) l = mid;
        else r = mid - 1;
    }
    return l;
}


4.浮点数二分法

bool check(double x) {/* ... */} // 检查x是否满足某种性质

double bsearch_3(double l, double r)
{
    const double eps = 1e-6;   // eps 表示精度，取决于题目对精度的要求
    while (r - l > eps)
    {
        double mid = (l + r) / 2;
        if (check(mid)) r = mid;
        else l = mid;
    }
    return l;
}